Perspective: Emergent topologies in oxide superlattices

Das, Sujit; Ghosh, Anirban; McCarter, Margaret R.; Hsu, Shang-Lin; Tang, Yun-Long; Damodaran, Anoop R.; Ramesh, R.; Martin, Lane W.

doi:10.1063/1.5046100

Title: Perspective: Emergent topologies in oxide superlattices

Journal Article · 23 October 2018 · APL Materials

DOI: https://doi.org/10.1063/1.5046100 · OSTI ID:1542321

Das, Sujit ^[1]; Ghosh, Anirban ^[1];

^[2];

^[3]; Tang, Yun-Long ^[4]; Damodaran, Anoop R. ^[1]; Ramesh, R. ^[5];

^[6]

Univ. of California, Berkeley, CA (United States). Dept. of Materials Science and Engineering
Univ. of California, Berkeley, CA (United States). Dept. of Physics
Univ. of California, Berkeley, CA (United States). Dept. of Materials Science and Engineering; Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Center for Electron Microscopy, Molecular Foundry
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division
Univ. of California, Berkeley, CA (United States). Dept. of Materials Science and Engineering; Univ. of California, Berkeley, CA (United States). Dept. of Physic; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division
Univ. of California, Berkeley, CA (United States). Dept. of Materials Science and Engineering; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division

The ability to synthesize high-quality, complex-oxide heterostructures has created a veritable playground in which to explore emergent phenomena and exotic phases which arise from the interplay of spin, charge, orbital, and lattice degrees of freedom. Of particular interest is the creation of artificial heterostructures and superlattices built from two or more materials. Through such approaches, it is possible to observe new phases and phenomena that are not present in the parent materials alone. This is especially true in ferroelectric materials where the appropriate choice of superlattice constituents can lead to structures with complex phase diagrams and rich physics. In this article, we review and explore future directions in such ferroic superlattices wherein recent studies have revealed complex emergent polarization topologies, novel states of matter, and intriguing properties that arise from our ability to manipulate materials with epitaxial strain, interfacial coupling and interactions, size effects, and more. We focus our attention on recent work in (PbTiO₃)_n/(SrTiO₃)_n superlattices wherein exotic polar-vortex structures have been observed. We review the history of these observations and highlights of recent studies and conclude with an overview and prospectus of how the field may evolve in the coming years.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1542321

Alternate ID(s):: OSTI ID: 1478684

Journal Information:: APL Materials, Journal Name: APL Materials Journal Issue: 10 Vol. 6; ISSN 2166-532X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (74)

Ferromagnetism in LaFeO3-LaCrO3 Superlattices Ueda, K. Science, Vol. 280, Issue 5366 https://doi.org/10.1126/science.280.5366.1064	journal	May 1998
A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface Ohtomo, A.; Hwang, H. Y. Nature, Vol. 427, Issue 6973 https://doi.org/10.1038/nature02308	journal	January 2004
Spontaneous Vortex Nanodomain Arrays at Ferroelectric Heterointerfaces Nelson, Christopher T.; Winchester, Benjamin; Zhang, Yi Nano Letters, Vol. 11, Issue 2 https://doi.org/10.1021/nl1041808	journal	February 2011
Enhanced Thermodynamic Stability of Epitaxial Oxide Thin Films Song, Jong Hyun; Susaki, Tomofumi; Hwang, Harold Y. Advanced Materials, Vol. 20, Issue 13 https://doi.org/10.1002/adma.200701919	journal	July 2008
Physics of thin-film ferroelectric oxides Dawber, M.; Rabe, K. M.; Scott, J. F. Reviews of Modern Physics, Vol. 77, Issue 4 https://doi.org/10.1103/revmodphys.77.1083	journal	October 2005
Direct observation of the spin structures of vortex domain walls in ferromagnetic nanowires Nagai, T.; Yamada, H.; Konoto, M. Physical Review B, Vol. 78, Issue 18 https://doi.org/10.1103/physrevb.78.180414	journal	November 2008
Polarization Rotation in Ferroelectric Tricolor PbTiO ₃ /SrTiO ₃ /PbZr _0.2 Ti _0.8 O ₃ Superlattices Lemée, Nathalie; Infante, Ingrid C.; Hubault, Cécile ACS Applied Materials & Interfaces, Vol. 7, Issue 36 https://doi.org/10.1021/acsami.5b03456	journal	August 2015
Original properties of dipole vortices in zero-dimensional ferroelectrics Prosandeev, S.; Ponomareva, I.; Naumov, I. Journal of Physics: Condensed Matter, Vol. 20, Issue 19 https://doi.org/10.1088/0953-8984/20/19/193201	journal	April 2008
Exotic Domain States in Ferroelectrics: Searching for Vortices and Skyrmions Gregg, J. M. Ferroelectrics, Vol. 433, Issue 1 https://doi.org/10.1080/00150193.2012.678131	journal	January 2012
Superconducting Interfaces Between Insulating Oxides Reyren, N.; Thiel, S.; Caviglia, A. D. Science, Vol. 317, Issue 5842 https://doi.org/10.1126/science.1146006	journal	August 2007
Domain configurations of nanostructured Permalloy elements Gomez, R. D.; Luu, T. V.; Pak, A. O. Journal of Applied Physics, Vol. 85, Issue 8 https://doi.org/10.1063/1.370030	journal	April 1999
Atomistic theory of hybrid improper ferroelectricity in perovskites Zhao, Hong Jian; Íñiguez, Jorge; Ren, Wei Physical Review B, Vol. 89, Issue 17 https://doi.org/10.1103/physrevb.89.174101	journal	May 2014
Piezo-Electric and Allied Phenomena in Rochelle Salt Valasek, J. Physical Review, Vol. 17, Issue 4 https://doi.org/10.1103/PhysRev.17.475	journal	April 1921
Emergent phenomena at oxide interfaces Hwang, H. Y.; Iwasa, Y.; Kawasaki, M. Nature Materials, Vol. 11, Issue 2 https://doi.org/10.1038/nmat3223	journal	January 2012
Strain Tuning of Ferroelectric Thin Films Schlom, Darrell G.; Chen, Long-Qing; Eom, Chang-Beom Annual Review of Materials Research, Vol. 37, Issue 1 https://doi.org/10.1146/annurev.matsci.37.061206.113016	journal	August 2007
Erratum: Giant Electroresistance in Ferroelectric Tunnel Junctions [Phys. Rev. Lett. 94 , 246802 (2005)] Zhuravlev, M. Ye.; Sabirianov, R. F.; Jaswal, S. S. Physical Review Letters, Vol. 102, Issue 16 https://doi.org/10.1103/physrevlett.102.169901	journal	April 2009
Characteristics and signatures of dipole vortices in ferroelectric nanodots: First-principles-based simulations and analytical expressions Prosandeev, S.; Bellaiche, L. Physical Review B, Vol. 75, Issue 9 https://doi.org/10.1103/physrevb.75.094102	journal	March 2007
A strategy for the design of skyrmion racetrack memories Tomasello, R.; Martinez, E.; Zivieri, R. Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep06784	journal	October 2014
Strong polarization enhancement in asymmetric three-component ferroelectric superlattices Lee, Ho Nyung; Christen, Hans M.; Chisholm, Matthew F. Nature, Vol. 433, Issue 7024 https://doi.org/10.1038/nature03261	journal	January 2005
Toroidal Ferroelectricity in PbTiO 3 Nanoparticles Stachiotti, M. G.; Sepliarsky, M. Physical Review Letters, Vol. 106, Issue 13 https://doi.org/10.1103/physrevlett.106.137601	journal	March 2011
Oxide Interfaces--An Opportunity for Electronics Mannhart, J.; Schlom, D. G. Science, Vol. 327, Issue 5973, p. 1607-1611 https://doi.org/10.1126/science.1181862	journal	March 2010
Imaging of spin dynamics in closure domain and vortex structures Park, J. P.; Eames, P.; Engebretson, D. M. Physical Review B, Vol. 67, Issue 2 https://doi.org/10.1103/physrevb.67.020403	journal	January 2003
Ferroelectric Domains in PbTiO ₃ /SrTiO ₃ Superlattices Zubko, P.; Jecklin, N.; Stucki, N. Ferroelectrics, Vol. 433, Issue 1 https://doi.org/10.1080/00150193.2012.678159	journal	January 2012
Emergent chirality in the electric polarization texture of titanate superlattices Shafer, Padraic; García-Fernández, Pablo; Aguado-Puente, Pablo Proceedings of the National Academy of Sciences, Vol. 115, Issue 5 https://doi.org/10.1073/pnas.1711652115	journal	January 2018
Phase coexistence and electric-field control of toroidal order in oxide superlattices Damodaran, A. R.; Clarkson, J. D.; Hong, Z. Nature Materials, Vol. 16, Issue 10 https://doi.org/10.1038/nmat4951	journal	August 2017
Three-dimensional magnetic-flux-closure patterns in mesoscopic Fe islands Hertel, R.; Fruchart, O.; Cherifi, S. Physical Review B, Vol. 72, Issue 21 https://doi.org/10.1103/physrevb.72.214409	journal	December 2005
Magnetic control of ferroelectric polarization Kimura, T.; Goto, T.; Shintani, H. Nature, Vol. 426, Issue 6962 https://doi.org/10.1038/nature02018	journal	November 2003
Use of Negative Capacitance to Provide Voltage Amplification for Low Power Nanoscale Devices Salahuddin, Sayeef; Datta, Supriyo Nano Letters, Vol. 8, Issue 2 https://doi.org/10.1021/nl071804g	journal	February 2008
Unusual Behavior of the Ferroelectric Polarization in PbTiO 3 / SrTiO 3 Superlattices Dawber, M.; Lichtensteiger, C.; Cantoni, M. Physical Review Letters, Vol. 95, Issue 17 https://doi.org/10.1103/physrevlett.95.177601	journal	October 2005
Jahn-Teller distortions induced by tetrahedral-site Fe2+ ions Goodenough, John B. Journal of Physics and Chemistry of Solids, Vol. 25, Issue 2 https://doi.org/10.1016/0022-3697(64)90073-3	journal	February 1964
Improper ferroelectricity in perovskite oxide artificial superlattices Bousquet, Eric; Dawber, Matthew; Stucki, Nicolas Nature, Vol. 452, Issue 7188 https://doi.org/10.1038/nature06817	journal	April 2008
Real-space observation of a two-dimensional skyrmion crystal Yu, X. Z.; Onose, Y.; Kanazawa, N. Nature, Vol. 465, Issue 7300 https://doi.org/10.1038/nature09124	journal	June 2010
Magnetic Domain-Wall Racetrack Memory Parkin, S. S. P.; Hayashi, M.; Thomas, L. Science, Vol. 320, Issue 5873, p. 190-194 https://doi.org/10.1126/science.1145799	journal	April 2008
Electrical switching of the vortex core in a magnetic disk Yamada, Keisuke; Kasai, Shinya; Nakatani, Yoshinobu Nature Materials, Vol. 6, Issue 4 https://doi.org/10.1038/nmat1867	journal	March 2007
Unusual phase transitions in ferroelectric nanodisks and nanorods Naumov, Ivan I.; Bellaiche, L.; Fu, Huaxiang Nature, Vol. 432, Issue 7018 https://doi.org/10.1038/nature03107	journal	December 2004
Geometric frustration in compositionally modulated ferroelectrics Choudhury, Narayani; Walizer, Laura; Lisenkov, Sergey Nature, Vol. 470, Issue 7335 https://doi.org/10.1038/nature09752	journal	February 2011
Observation of polar vortices in oxide superlattices Yadav, A. K.; Nelson, C. T.; Hsu, S. L. Nature, Vol. 530, Issue 7589 https://doi.org/10.1038/nature16463	journal	January 2016
Some symmetry aspects of ferroics and single phase multiferroics ^* Schmid, Hans Journal of Physics: Condensed Matter, Vol. 20, Issue 43 https://doi.org/10.1088/0953-8984/20/43/434201	journal	October 2008
Strain dependence of antiferromagnetic interface coupling in La 0.7 Sr 0.3 MnO 3 / SrRuO 3 superlattices Das, Sujit; Herklotz, Andreas; Pippel, Eckhard Physical Review B, Vol. 91, Issue 13 https://doi.org/10.1103/physrevb.91.134405	journal	April 2015
Ferroelectric-field-induced tuning of magnetism in the colossal magnetoresistive oxide La 1 − x Sr x MnO 3 Hong, X.; Posadas, A.; Lin, A. Physical Review B, Vol. 68, Issue 13 https://doi.org/10.1103/physrevb.68.134415	journal	October 2003
Magnetic phase control by an electric field Lottermoser, Thomas; Lonkai, Thomas; Amann, Uwe Nature, Vol. 430, Issue 6999 https://doi.org/10.1038/nature02728	journal	July 2004
Ferroelectricity in Barium Titanate Quantum Dots and Wires Fu, Huaxiang; Bellaiche, L. Physical Review Letters, Vol. 91, Issue 25 https://doi.org/10.1103/physrevlett.91.257601	journal	December 2003
Deterministic control of magnetic vortex wall chirality by electric field Beardsley, R. P.; Bowe, S.; Parkes, D. E. Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-07944-9	journal	August 2017
X-Ray Diffraction Studies of 180° Ferroelectric Domains in PbTiO 3 / SrTiO 3 Superlattices under an Applied Electric Field Zubko, P.; Stucki, N.; Lichtensteiger, C. Physical Review Letters, Vol. 104, Issue 18 https://doi.org/10.1103/physrevlett.104.187601	journal	May 2010
Skyrmion Lattice in a Chiral Magnet Muhlbauer, S.; Binz, B.; Jonietz, F. Science, Vol. 323, Issue 5916 https://doi.org/10.1126/science.1166767	journal	February 2009
Topological Structures in Multiferroics - Domain Walls, Skyrmions and Vortices Seidel, Jan; Vasudevan, Rama K.; Valanoor, Nagarajan Advanced Electronic Materials, Vol. 2, Issue 1 https://doi.org/10.1002/aelm.201500292	journal	December 2015
Electric-field control of local ferromagnetism using a magnetoelectric multiferroic Chu, Ying-Hao; Martin, Lane W.; Holcomb, Mikel B. Nature Materials, Vol. 7, Issue 6, p. 478-482 https://doi.org/10.1038/nmat2184	journal	April 2008
Direct observation of the alignment of ferromagnetic spins by antiferromagnetic spins Nolting, F.; Scholl, A.; Stöhr, J. Nature, Vol. 405, Issue 6788 https://doi.org/10.1038/35015515	journal	June 2000
Flux-closure-domain states and demagnetizing energy determination in sub-micron size magnetic dots Jubert, P. -O; Toussaint, J. -C; Fruchart, O. Europhysics Letters (EPL), Vol. 63, Issue 1 https://doi.org/10.1209/epl/i2003-00488-0	journal	July 2003
Negative capacitance in multidomain ferroelectric superlattices Zubko, Pavlo; Wojdeł, Jacek C.; Hadjimichael, Marios Nature, Vol. 534, Issue 7608 https://doi.org/10.1038/nature17659	journal	June 2016
Chiral Patterns of Tilting of Oxygen Octahedra in Zero-Dimensional Ferroelectrics and Multiferroics: A First Principle-Based Study Sichuga, David; Ren, Wei; Prosandeev, Sergey Physical Review Letters, Vol. 104, Issue 20 https://doi.org/10.1103/physrevlett.104.207603	journal	May 2010
Magnetic domains in epitaxial nanomagnets with uniaxial or fourfold crystal anisotropy Pulwey, R.; Zölfl, M.; Bayreuther, G. Journal of Applied Physics, Vol. 91, Issue 10 https://doi.org/10.1063/1.1453339	journal	January 2002
The topological theory of defects in ordered media Mermin, N. D. Reviews of Modern Physics, Vol. 51, Issue 3 https://doi.org/10.1103/revmodphys.51.591	journal	July 1979
Physical Theory of Ferromagnetic Domains Kittel, Charles Reviews of Modern Physics, Vol. 21, Issue 4 https://doi.org/10.1103/revmodphys.21.541	journal	October 1949
Positive exchange bias in ferromagnetic La0.67Sr0.33MnO3∕SrRuO3 bilayers Ke, X.; Rzchowski, M. S.; Belenky, L. J. Applied Physics Letters, Vol. 84, Issue 26 https://doi.org/10.1063/1.1767955	journal	June 2004
Natural optical activity and its control by electric field in electrotoroidic systems Prosandeev, Sergey; Malashevich, Andrei; Gui, Zhigang Physical Review B, Vol. 87, Issue 19 https://doi.org/10.1103/physrevb.87.195111	journal	May 2013
Magnetic Vortex Core Observation in Circular Dots of Permalloy Shinjo, T. Science, Vol. 289, Issue 5481 https://doi.org/10.1126/science.289.5481.930	journal	August 2000
Formation of artificial BaTiO ₃ /SrTiO ₃ superlattices using pulsed laser deposition and their dielectric properties Tabata, Hitoshi; Tanaka, Hidekazu; Kawai, Tomoji Applied Physics Letters, Vol. 65, Issue 15 https://doi.org/10.1063/1.112837	journal	October 1994
Electrostatic Coupling and Local Structural Distortions at Interfaces in Ferroelectric/Paraelectric Superlattices Zubko, P.; Jecklin, N.; Torres-Pardo, A. Nano Letters, Vol. 12, Issue 6 https://doi.org/10.1021/nl3003717	journal	May 2012
Observation of Nanoscale 180 ° Stripe Domains in Ferroelectric P b T i O 3 Thin Films Streiffer, S. K.; Eastman, J. A.; Fong, D. D. Physical Review Letters, Vol. 89, Issue 6 https://doi.org/10.1103/physrevlett.89.067601	journal	July 2002
Control of the chirality and polarity of magnetic vortices in triangular nanodots Jaafar, M.; Yanes, R.; Perez de Lara, D. Physical Review B, Vol. 81, Issue 5 https://doi.org/10.1103/physrevb.81.054439	journal	February 2010
Evidence for Pb-O Covalency in Tetragonal PbTiO 3 Kuroiwa, Yoshihiro; Aoyagi, Shinobu; Sawada, Akikatsu Physical Review Letters, Vol. 87, Issue 21 https://doi.org/10.1103/physrevlett.87.217601	journal	November 2001
L'hypothèse du champ moléculaire et la propriété ferromagnétique Weiss, Pierre Journal de Physique Théorique et Appliquée, Vol. 6, Issue 1 https://doi.org/10.1051/jphystap:019070060066100	journal	January 1907
Ultrathin oxide films and interfaces for electronics and spintronics Bibes, Manuel; Villegas, Javier E.; Barthélémy, Agnès Advances in Physics, Vol. 60, Issue 1 https://doi.org/10.1080/00018732.2010.534865	journal	February 2011
Exchange bias in LaNiO3–LaMnO3 superlattices Gibert, Marta; Zubko, Pavlo; Scherwitzl, Raoul Nature Materials, Vol. 11, Issue 3 https://doi.org/10.1038/nmat3224	journal	January 2012
SrTi O 3 : An intrinsic quantum paraelectric below 4 K Müller, K. A.; Burkard, H. Physical Review B, Vol. 19, Issue 7 https://doi.org/10.1103/physrevb.19.3593	journal	April 1979
Discovery of stable skyrmionic state in ferroelectric nanocomposites Nahas, Y.; Prokhorenko, S.; Louis, L. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9542	journal	October 2015
Predicted Magnetoelectric Effect in Fe / BaTiO 3 Multilayers: Ferroelectric Control of Magnetism Duan, Chun-Gang; Jaswal, S. S.; Tsymbal, E. Y. Physical Review Letters, Vol. 97, Issue 4 https://doi.org/10.1103/physrevlett.97.047201	journal	July 2006
Electrical Manipulation of Magnetization Reversal in a Ferromagnetic Semiconductor Chiba, D. Science, Vol. 301, Issue 5635 https://doi.org/10.1126/science.1086608	journal	August 2003
Ferroelectricity in Ultrathin Perovskite Films Fong, Dillon D.; Stephenson, G. Brian; Streiffer, Stephen K. Science, Vol. 304, Issue 5677, p. 1650-1653 https://doi.org/10.1126/science.1098252	journal	June 2004
Observation of a periodic array of flux-closure quadrants in strained ferroelectric PbTiO3 films Tang, Y. L.; Zhu, Y. L.; Ma, X. L. Science, Vol. 348, Issue 6234 https://doi.org/10.1126/science.1259869	journal	April 2015
Colossal Magnetoresistive Oxides Tokura, Yoshinori https://doi.org/10.1201/9781482287493	book	April 2014
Enhancement of ferroelectricity at metal–oxide interfaces Stengel, Massimiliano; Vanderbilt, David; Spaldin, Nicola A. Nature Materials, Vol. 8, Issue 5 https://doi.org/10.1038/nmat2429	journal	April 2009
Direct Observation of Continuous Electric Dipole Rotation in Flux-Closure Domains in Ferroelectric Pb(Zr,Ti)O3 Jia, C. -L.; Urban, K. W.; Alexe, M. Science, Vol. 331, Issue 6023 https://doi.org/10.1126/science.1200605	journal	March 2011

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